Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest.
$\left[ \begin{array} { c c c }
- 1 & 0 & - 1 \
0 & 1 & 0 \
1 & 2 & - 2
\end{array} \right]$
A) 3
B) $- 1$
C) $- 3$
D) $2$
E) $1$

Question

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest. 
$\left[ \begin{array} { c c c } 
- 1 & 0 & - 1 \
0 & 1 & 0 \
1 & 2 & - 2
\end{array} \right]$
A) 3
B) $- 1$
C) $- 3$
D) $2$
E) $1$

Quizplus · Accepted Answer

Expanding along the second row, which contains two zeros, simplifies the calculation. The determinant is $0*(-1)^{2+1}*\left|\begin{array}{cc}0 & -1 \ 2 & -2\end{array}\right| + 1*(-1)^{2+2}*\left|\begin{array}{cc}-1 & -1 \ 1 & -2\end{array}\right| = 0 + 1*((-1)*(-2) - (-1)*1) = 1*(2+1) = 3.$

Evaluate the Determinant of the Matrix [−10−101012−2]\left[ \begin{array} { c c c } - 1 & 0 & - 1 \\0 & 1 & 0 \\1 & 2 & - 2\end{array} \right]​−101​012​−10−2​​

Evaluate the Determinant of the Matrix $\left[ \begin{array} { c c c } - 1 & 0 & - 1 \\0 & 1 & 0 \\1 & 2 & - 2\end{array} \right]$